Details

analyze2.1s (31.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
1.6%	98.1%	0.3%	13
2.3%	97.4%	0.3%	14

Compiler

Compiled 24 to 18 computations (25% saved)

sample2.0s (29.9%)

Symmetry

(sort y z t)

(sort a b)

Results

1.3s	8256×	body	128	valid
486.0ms	2973×	body	128	invalid

Compiler

Compiled 71 to 53 computations (25.4% saved)

simplify73.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

712×	`fma-neg_binary64`
641×	`fma-def_binary64`
213×	`cancel-sign-sub-inv_binary64`
172×	`distribute-rgt-neg-in_binary64`
157×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	25
1	39	23
2	115	21
3	308	21
4	552	21
5	902	21
6	1201	21
7	1433	21
8	1672	21
9	1787	21
10	1791	21
11	1791	21
12	1791	21
13	1674	21

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	2.2b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	2.9b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))

Compiler

Compiled 126 to 90 computations (28.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x 2 (.f64 (.f64 a 27) b))
✓	0.2b	(.f64 (.f64 z t) -9)
✓	0.2b	(.f64 (.f64 a 27) b)
✓	2.0b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))

series50.0ms (0.7%)

Counts

4 → 156

Calls

4 calls:

32.0ms	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
9.0ms	(fma.f64 x 2 (.f64 (.f64 a 27) b))
5.0ms	(.f64 (.f64 z t) -9)
4.0ms	(.f64 (.f64 a 27) b)

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
14×	`pow1_binary64`
6×	`associate-r_binary64`
6×	`cbrt-unprod_binary64`

Counts

4 → 60

Calls

4 calls:

4.0ms	(.f64 (.f64 a 27) b)
4.0ms	(.f64 (.f64 z t) -9)
0.0ms	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
0.0ms	(fma.f64 x 2 (.f64 (.f64 a 27) b))

simplify99.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

868×	`unswap-sqr_binary64`
419×	`*-commutative_binary64`
321×	`distribute-lft-in_binary64`
321×	`distribute-rgt-in_binary64`
310×	`fma-def_binary64`

Counts

216 → 107

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	122	2976
1	250	2724
2	873	2724
3	1485	2724
4	2922	2724
5	5289	2724

prune101.0ms (1.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	102	5	107
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	103	6	109

Error

0.0b

Counts

109 → 6

Alt Table

Status	Error	Program
	2.2b	(fma.f64 y (.f64 z (.f64 t -9)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	2.5b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (.f64 (.f64 z t) -9)) (cbrt.f64 (.f64 (.f64 z t) -9))) (cbrt.f64 (.f64 (.f64 z t) -9))) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
▶	1.9b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
	2.2b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))
	40.3b	(cbrt.f64 (.f64 (.f64 (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b))) (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))) (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))))
	2.9b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))

Compiler

Compiled 2454 to 1418 computations (42.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 2 x (.f64 (.f64 y (*.f64 t z)) -9))
✓	0.1b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
✓	0.3b	(.f64 (.f64 y (*.f64 t z)) -9)
✓	6.1b	(.f64 y (.f64 t z))

series73.0ms (1.1%)

Counts

4 → 156

Calls

4 calls:

35.0ms	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
17.0ms	(fma.f64 2 x (.f64 (.f64 y (*.f64 t z)) -9))
10.0ms	(.f64 (.f64 y (*.f64 t z)) -9)
10.0ms	(.f64 y (.f64 t z))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-cbrt-cube_binary64`
18×	`add-exp-log_binary64`
18×	`pow1_binary64`
9×	`cbrt-unprod_binary64`
9×	`prod-exp_binary64`

Counts

4 → 63

Calls

4 calls:

5.0ms	(.f64 (.f64 y (*.f64 t z)) -9)
4.0ms	(.f64 y (.f64 t z))
0.0ms	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
0.0ms	(fma.f64 2 x (.f64 (.f64 y (*.f64 t z)) -9))

simplify121.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

507×	`distribute-rgt-in_binary64`
501×	`distribute-lft-in_binary64`
416×	`fma-def_binary64`
360×	`*-commutative_binary64`
190×	`associate-+l+_binary64`

Counts

219 → 94

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	103	3305
1	213	3114
2	739	3114
3	1576	3114
4	4976	3114
5	4981	3114

prune90.0ms (1.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	92	2	94
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	93	7	100

Error

0.0b

Counts

100 → 7

Alt Table

Status	Error	Program
	2.2b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))
	4.4b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 (.f64 y t) z) -9)))
▶	2.2b	(fma.f64 y (.f64 z (.f64 t -9)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	2.5b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (.f64 (.f64 z t) -9)) (cbrt.f64 (.f64 (.f64 z t) -9))) (cbrt.f64 (.f64 (.f64 z t) -9))) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
✓	1.9b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
	31.9b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (cbrt.f64 (.f64 (.f64 (.f64 y y) y) (.f64 (.f64 (.f64 t z) (.f64 t z)) (.f64 t z)))) -9)))
	2.9b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))

Compiler

Compiled 2270 to 1105 computations (51.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 x 2 (.f64 (.f64 a 27) b))
✓	0.2b	(.f64 z (.f64 t -9))
	0.2b	(.f64 (.f64 a 27) b)
✓	2.0b	(fma.f64 y (.f64 z (.f64 t -9)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))

series40.0ms (0.6%)

Counts

2 → 96

Calls

2 calls:

34.0ms	(fma.f64 y (.f64 z (.f64 t -9)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
6.0ms	(.f64 z (.f64 t -9))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
3×	`associate-l_binary64`
3×	`cbrt-unprod_binary64`

Counts

2 → 30

Calls

2 calls:

4.0ms	(.f64 z (.f64 t -9))
0.0ms	(fma.f64 y (.f64 z (.f64 t -9)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))

simplify108.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

518×	`distribute-lft-in_binary64`
518×	`distribute-rgt-in_binary64`
508×	`associate-l_binary64`
374×	`fma-neg_binary64`
362×	`associate-r_binary64`

Counts

126 → 60

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	73	2086
1	153	1893
2	434	1893
3	1359	1893
4	3924	1893
5	4790	1893
6	5038	1893

prune102.0ms (1.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	107	7	114

Error

0.0b

Counts

114 → 7

Alt Table

Status	Error	Program
▶	2.2b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))
	4.4b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 (.f64 y t) z) -9)))
✓	2.2b	(fma.f64 y (.f64 z (.f64 t -9)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	2.5b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (.f64 (.f64 z t) -9)) (cbrt.f64 (.f64 (.f64 z t) -9))) (cbrt.f64 (.f64 (.f64 z t) -9))) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
✓	1.9b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
	31.9b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (cbrt.f64 (.f64 (.f64 (.f64 y y) y) (.f64 (.f64 (.f64 t z) (.f64 t z)) (.f64 t z)))) -9)))
	2.9b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))

Compiler

Compiled 2414 to 1456 computations (39.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x 2 (.f64 a (.f64 27 b)))
	0.2b	(.f64 (.f64 z t) -9)
✓	0.2b	(.f64 a (.f64 27 b))
✓	2.0b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))

series46.0ms (0.7%)

Counts

3 → 132

Calls

3 calls:

34.0ms	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))
7.0ms	(fma.f64 x 2 (.f64 a (.f64 27 b)))
5.0ms	(.f64 a (.f64 27 b))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`

Counts

3 → 40

Calls

3 calls:

9.0ms	(.f64 a (.f64 27 b))
0.0ms	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))
0.0ms	(fma.f64 x 2 (.f64 a (.f64 27 b)))

simplify105.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

576×	`distribute-lft-in_binary64`
576×	`distribute-rgt-in_binary64`
548×	`associate-l_binary64`
426×	`fma-def_binary64`
385×	`associate-r_binary64`

Counts

172 → 77

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	82	2594
1	159	2378
2	475	2378
3	1528	2378
4	4509	2378
5	5090	2378

prune92.0ms (1.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	106	8	114

Error

0.0b

Counts

114 → 8

Alt Table

Status	Error	Program
✓	2.2b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))
	4.4b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 (.f64 y t) z) -9)))
	2.9b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
	50.8b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (sqrt.f64 a) (.f64 (sqrt.f64 a) (*.f64 27 b)))))
✓	2.2b	(fma.f64 y (.f64 z (.f64 t -9)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	2.5b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (.f64 (.f64 z t) -9)) (cbrt.f64 (.f64 (.f64 z t) -9))) (cbrt.f64 (.f64 (.f64 z t) -9))) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
✓	1.9b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
	31.9b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (cbrt.f64 (.f64 (.f64 (.f64 y y) y) (.f64 (.f64 (.f64 t z) (.f64 t z)) (.f64 t z)))) -9)))

Compiler

Compiled 2304 to 1315 computations (42.9% saved)

regimes759.0ms (11.1%)

Accuracy

Total 0.6b remaining (96.3%)

Threshold costs 0.6b (96.3%)

Counts

36 → 2

Compiler

Compiled 12940 to 9115 computations (29.6% saved)

bsearch43.0ms (0.6%)

Steps

Iters	Range		Point
7	2.3855949512714515e+46	1.7379739630019135e+51	1.5495380779881153e+51

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary64`
8×	`+-commutative_binary64`
7×	`sub-neg_binary64`
6×	`distribute-rgt-neg-in_binary64`
6×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	52
1	45	52
2	61	52
3	77	52
4	87	52
5	92	52
6	93	52
7	92	52

end659.0ms (9.7%)

Remove: (sort a b)
Compiler: Compiled 538 to 370 computations (31.2% saved)

Details

analyze2.1s (31.2%)

sample2.0s (29.9%)

simplify73.0ms (1.1%)

prune4.0ms (0.1%)

localize12.0ms (0.2%)

series50.0ms (0.7%)

rewrite10.0ms (0.1%)

simplify99.0ms (1.5%)

prune101.0ms (1.5%)

localize11.0ms (0.2%)

series73.0ms (1.1%)

rewrite12.0ms (0.2%)

simplify121.0ms (1.8%)

prune90.0ms (1.3%)

localize11.0ms (0.2%)

series40.0ms (0.6%)

rewrite5.0ms (0.1%)

simplify108.0ms (1.6%)

prune102.0ms (1.5%)

localize11.0ms (0.2%)

series46.0ms (0.7%)

rewrite11.0ms (0.2%)

simplify105.0ms (1.5%)

prune92.0ms (1.4%)

regimes759.0ms (11.1%)

bsearch43.0ms (0.6%)

simplify5.0ms (0.1%)

end659.0ms (9.7%)

Profiling